The massless modular Hamiltonian
Abstract
We compute the vacuum local modular Hamiltonian associated with a space ball region in the free scalar massless Quantum Field Theory. We give an explicit expression on the one particle Hilbert space in terms of the higher dimensional Legendre differential operator. The quadratic form of the massless modular Hamiltonian is expressed in terms of an integral of the energy density with the parabolic distribution. We then get the formula for the local entropy of a wave packet. This gives the vacuum relative entropy of a coherent state on the double cone von Neumann algebras associated with the free scalar QFT. Among other points, we provide the passivity characterisation of the modular Hamiltonian within the standard subspace setup.
Keywords
Cite
@article{arxiv.2012.00565,
title = {The massless modular Hamiltonian},
author = {Roberto Longo and Gerardo Morsella},
journal= {arXiv preprint arXiv:2012.00565},
year = {2022}
}
Comments
Changes w.r.t. v. 3: only this comment. Changes w.r.t. v. 2: the results on the massive modular hamiltonian of a ball contained a gap, and have been removed. 23 pages, 1 figure